The entire plate comes off by removing 2 more larger screws on the back edge and sliding the whole thing back about 1/2".
Since I assume the fan switch was ruined by grease penetration, the escutcheon is likely also glued down with the stuff. With the back screws removed, slide the thing back towards the fan opening and lift it up. Use a de-greaser spray around the egdes first if you so desire. I guess it goes without saying, but always disconnect the power before doing something like this.
The last words every redneck says before dying..."Hey, ya'll...watch this